Fundamental Limitations on Instrumental Precision

Because of doubt about the weighing error and the temperature correction, it was necessary to repeat the determination see the results given in Example 1 on p. 56. The new value of [aJo was +152.61 0.23 deg dm (g cm. Evidently the optical purity of the specimen was quite high the difference from the literature value of +152.70 is not significant at the 95 percent confidence level. 

Final Caution. The Student t distribution is to be used when the numerical value to which it attaches is a mean of a definite number of direct observations or is a numerical result calculated from such a mean by a procedure that introduces no uncertainties comparable in magnitude to the random errors of the direct observations. This is notihe case for the specific rotation [a]j discussed above. The uncertainty contribution to the final result that is due to random errors in the raw data on optical rotations Oy is not large compared to the contributions due to the estimated uncertainties in the other variables (particularly Vand Z) that are required for calculating the final result The number of degrees of 

An electrical measuring instrument contains electrical circuits incorporating capacitance, inductance, and resistance. In the absence of resistance, a circuit tends to oscillate with a definite frequency /when disturbed. For optimum performance an amount of resistance is incorporated that is barely sufficient to damp the oscillations resulting from transient inputs the circuit is then said to be critically damped. For a critically damped circuit it can be shown that the root-mean-square (rms) fluctuations in voltage V and in current /are given by 

An important limitation that is sometimes encountered is due to the particulate nature of electricity (electrons, ions) and of radiation (photons). The measurement of radiation intensities is in certain cases (e.g., X rays) performed by counting particles or photons one at a time. The number A counted in a time interval of given magnitude is subject to statistical fluctuations a count of A is subject to an estimated standard error given by 

The only way to overcome limitations imposed by the particulate nature of electricity and radiation is to scale up the experiment in physical size, time span, or intensity, all 

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